It is commonly believed that the visual motion signals are used to predict the future position of a moving target. Yet, the signals that drive the oculomotor system actually correspond to an estimate of target position expected here-and-now rather than an estimate of any undefined future position (Fleuriet & Goffart 2012). Therefore, we searched for the extrapolation limits and found that this estimate requires learning. First, we studied saccades toward a target moving horizontally in the upper/lower visual field for durations that gradually increased from 50 to 800 ms. The short motion triggered saccades but no pursuit. Control saccades toward static targets were also recorded as a baseline to reveal an extrapolation that was rather limited. After the progressive training, saccades were followed by smooth tracking at the longest duration (Bourrelly et al. VSS 2014). Following this training, short duration stimuli still triggered saccades without pursuit. We next studied "occlusion" training starting with the 800 ms motion, but then introducing a short occlusion in the middle of the trajectory. Over consecutive days of training, the occlusion was increased in duration from 100 to 300 ms. Gradually, pursuit-like tracking appeared during the occlusion, even though the initial segment of visible motion was still only 100 to 200 ms, a duration which did not trigger pursuit in the first experiment. We then tested the initial motion segments with no subsequent reappearance and found that now the saccades were followed by a slow pursuit-like eye movement, as if the monkeys were tracking an invisible target. Our work shows the limits of extrapolation within the visuo-oculomotor system. The signals that encode the spatiotemporal trajectory and drive the on-going tracking behavior mostly result from interpolation mechanisms. Our research should allow identifying the neural channels by which the mnemonic signals dynamically guide the on-going tracking response.